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20 [9] A. Greenbaum. Parallelizing the adaptive fast multipole method on a shared memory MIMD machine. NYU Ultracomputer Note 162, June 1989. [14] T. Hrycak and V. Rokhlin. An improved fast multipole algorithm for potential fields. [17] Yu Hu and S. Lennart Johnsson. A data-parallel implementation of hierarchical N-body methods. A parallel adaptive fast multipole algorithm for N-body problems. A data-parallel implementation of the adaptive fast multipole algorithm. 19 versions of FMM and Anderson's Method. A more detailed study is needed in order to assess the advantages and disadvantages of the different methods. Such a study would also have to include the recent algorithm of Hrycak and Rokhlin [14], which may give significant performance gains over the other methods. An interesting question in the context of such a comparative study is how to best optimize these methods for current CPUs and memory systems. While we have made an effort to achieve efficiency in our codes, additional improvements are certainly possible, e.g., by carefully tuning for the memory hierarchy. Finally, it would be interesting to see how our techniques and implementations perform on a real application domain. References [1] C. Anderson. An implementation of the fast multipole method without multipoles. SIAM J. of multipole-based algorithms for molecular dynamics applications. Table 6.8: Memory usage in bytes as a function of the number of particles, for 16 processors estimate as the precise ratio depends on the memory consumption of the sequential code on the same number of particles, which we could not measure.) Note that our numbers are based on a 1-separation criterium, and that they will get worse in the case of 2-separation. We have also not included the numbers for Barnes-Hut, which are slightly better then those for Anderson and FMM. Finally, the amount of communication in the replication phase is roughly equivalent to the size of the replicated bodies and nodes. However, we found the cost of transmitting the data over the network to be quite small, even if we include the (usually slightly larger) computational cost of inserting the received data into the tree structures. In this paper, we have described portable and efficient parallel implementations of several adaptive N-body methods, including the adaptive FMM and the adaptive version of Anderson's Method. Our experimental results demonstrate that our codes achieve high performance and efficient speed-up across several classes of parallel architectures. A downside of our implementations are the significant …

Highly Portable and Efficient Implementations of Parallel Adaptive N-Body Methods